You could create a user group with the rights to install that specific
product, but I think that you'd need to be adept with Windows user management
as well as with Windows registry permissions. I would think that an easier
resolution to this problem would be to install Adobe Reader on all of the
relevant computers using your administrator account.

I might have miss-interpreted your question, but It sounds to me as if the
"associated" application with the .pdf extension is pointing to the
installation executable and not the adobe reader.

I'd check by browsing to the C:\Program Files\Adobe\Acrobat 6.0\Reader
directory and locating the proper executable. (in the above case
AcroRd32.exe.)

locate a pdf file like C:\Program Files\Adobe\Acrobat 6.0\Help\ENU\Reader.pdf
right click on it, select "Open With, Choose Program" Browse to the Adobe
Acrobat reader AcroRd32.exe or equivelent in your version.  

After this is set on the user workstation (of course appropriate rights are
required to make such adjustments) the subsequent double clicking on .pdf
files should execute the start of the reader and not the start of the
installation of the reader.